Provincial composite economic indicators

Philip Smith (@PhilSmith26)

October 13, 2020

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The monthly provincial composite economic indicators (PCEIs) are summary measures based on 50-60 time series in each of the ten provinces. The time series are sourced in Statistics Canada’s online database, known these days variously as the NDM (“New Data Model”) or CODR (“Canadian Online Data Repository”) and formerly known as CANSIM. The PCEIs are similar to indicators produced and updated regularly by the Chicago Federal Reserve for the US economy, Professor Trevor Tombe for the Alberta economy, Brendon Ogmundson for the BC economy and the New Zealand Treasury for the New Zealand economy. Eswar Prasad, Darren Chang and Ethan Wu at the Brookings Institution are using the same methodological approach to calculate their composite indexes for tracking the global economic recovery. The methodology is endorsed by the OECD and the United Nations Economic Commission for Europe


The PCEI for a particular province shows how rapidly the 50-60 provincial time series are growing relative to the trend real growth rate in that province, collectively, while abstracting from the many other sources of mostly short-term variation affecting the indicators such as survey sampling and other error and unusual weather. The PCEIs are interpreted as gauges of overall performance in the economies of the provinces.


Why 50-60 time series? 

There is really no upper limit on the number of time series that can be used in the analysis, but there are very likely to be, at some point, diminishing returns as more time series are added. The only practical constraints are (1) the limited number of relevant time series that are available monthly and on a timely basis in a given province and (2) the work involved in managing larger numbers of time series. There tend to be somewhat fewer monthly economic time series available to choose from in the case of a smaller Canadian province, since there is typically less industrial diversification and confidentiality restrictions can prevent statistical releases for some industries. The ten PCEIs have different numbers of time series indicators, mostly ranging from 50 to 60, with larger provinces usually having more indicators than smaller ones. The indicators are listed in the Annex below.


The time series are diverse and cannot be aggregated directly. They include numbers of persons employed, counts of hours worked or housing starts, and many others are indexes. Nevertheless, when considered  jointly they constitute a good, albeit far from perfect proxy for the overall economy. The challenge is to find a way to combine them in a single composite indicator.


Why not just use national accounts?

The best way to do this is through the framework of the international System of National Accounts. That framework provides a coherent, internationally accepted and time-tested set of statistics aggregating to gross domestic product (GDP). It contains lots of drill-down capacity and lengthy time series. Canada has one of the world’s best sets of national accounts and they provide monthly, quarterly and annual estimates of GDP at the national level. The accounts have been produced by Statistics Canada (formerly the Dominion Bureau of Statistics) since the late 1940s and some historical national accounts estimates have also been made by academics as far back as the late 1800s. However, provincial and territorial accounts are available only on an annual basis from 1981. It would be quite expensive, in terms both of money to pay statisticians and burden imposed on survey respondents, to develop and maintain good sub-annual estimates. In their absence, there is a need for other sub-annual measures of the overall direction of the provincial and territorial economies.


What is the calculation method exactly?

To calculate the PCEI for a given province, the 50-60 time series are de-trended by transforming from levels to either 1-month or 12-month growth rates. They are normalized by subtracting the mean growth rate and dividing by the standard deviation of the growth rate. The principal components of the time series so transformed are then calculated. The PCEI is the first principal component, which is the one accounting for more of the total variance in the 50-60 series than any of the other principal components. In the calculations discussed here, that has typically ranged between 15% and 30% of the variance. Provinces with larger economies typically have the larger percentages. This is because the signal-to-noise ratios are usually much lower in smaller provinces. 


The PCEIs are indexes

The PCEIs measure change, but not level. In other words, they are like the Consumer Price Index which has an arbitrary scale that is typically set to 100 in some year. They are not like nominal GDP, which has a well defined level in dollar terms, although they are like “real” Fisher-chained GDP volume in this respect. The PCEIs are best presented either as a series of percentage changes or, if they are de-trended with month-to-month percentage changes, linked together as an index set equal to 100 in some time period and driven forward and backward by the percentages on a cumulative basis. It should be noted, though, that if the month-to-month percentage changes are linked together to form a chain index, that index will tend to drift off the true path over time, just like any other chained index. For this reason, the PCEI indexes are best used for short-term analyses of a few months or perhaps a couple of years at most, and should be considered much less dependable for longer-term studies. 


De-trending with 12-month changes

When the monthly indicators are de-trended by calculating year-over-year (12-month) percentage changes, the resulting charts are smooth and easily interpretable because of the embodied correlation. This smoothness is illustrated in the chart below for Alberta.
















This PCEI chart shows how the recent COVID-19-related decline compares with the drops in 2015-2016 when world energy prices collapsed, and 2008-2009 when the entire world fell into recession. It also shows that the current Alberta economic downturn began in 2018 before intensifying in March 2020. The PCEI here is portrayed as deviations from trend growth, so if it is zero in a particular month, that means the provincial economy is growing at its normal trend rate. One measure of this trend is the average annual growth rate in real GDP between 2002 and 2018, which is 2.6%, although other measures of trend growth are certainly possible.


Allocating the indicators to groups

The chart above also shows how the 62 Alberta indicators are contributing to each month’s PCEI. The indicators are allocated to four groups, named “production”, “labour market”, “investment” and “household consumption and income”. This is a judgemental allocation and there could be more or fewer groups. The choice of which group to put each indicator in is debatable. A key and usually unanswerable question is whether a particular indicator most reflects supply or demand forces. But given a set of groups and allocations, since the PCEI itself is a weighted sum of the 62 de-trended and normalized indicators, it is straightforward to group this sum in four parts. These are the colour-coded components shown in the chart. This breakdown shows, among other things, that Alberta’s current economic downturn was evident in all four groups.


It is exceedingly difficult if not impossible to interpret the impact of a particular indicator on the PCEI. There is no economic theory in the calculation, beyond the choice of indicators. The principal components method determines an optimal set of weights, some of which are positive and others negative. While one might expect certain indicators to have positive (or negative) weights, that need not be the case. However, the movements of the groups can be more intuitive depending on how they are defined. That does seem to be the case in the chart. 


De-trending with 1-month changes

The next chart is comparable to the first one, except that de-trending is done 1-month instead of 12-month percentage changes. The smoothness seen in the first chart is gone, as expected. This is the kind of calculation that is more illuminating when the focus is very short-term in nature.
















The third chart below “zooms in” on the last five years and makes the detail for 2020 and the previous five years clearer. It shows the Covid-19 collapse in March and April followed by the rebound in May, June and July, with the labour market indicators group and to a lesser extent the household expenditure and income group as the dominating forces. There are some interesting patterns in the pre-2019 results also, although they are not as prominent.

















The PCEI sometimes gives a crystal clear picture, as during the great recession and subsequent recovery in which the indicator groups are near unanimous. However, it sometimes gives a more mixed picture with some component time series groups above trend and others below. When there is divergence among the indicators this of course reflects lack of clarity in the real-world picture.


Looking at all the indicators together

It is also illuminating to compare the PCEIs for the provinces, particularly in the light of the COVID-19 period that began in March 2020. Below is a table showing all ten PCEIs for the first seven months of 2020, along with a final column showing the cumulative percentage change since February. The calculations indicate that the economies of Saskatchewan and Prince Edward Island fared best over that period, while those of Ontario and British Columbia are hardest hit.






























In this table the aggregates for the regions and for Canada as a whole are calculated as weighted averages of the provincial indexes, with the weights being the average GDP shares between 2002 and 2018.


These ‘COVID-19 paths’ can also be illustrated graphically, as in the example for Atlantic Canada below, highlighting the superior economic performances of that region relative to Canada as a whole.

















Caveats

The PCEI itself is, of course, an imperfect indicator. There are under-represented sectors, due to a lack of monthly component time series. The mix of component series is imperfectly balanced and there is no role for economic theory aside from the choice of component series and groups. The interpretation of the first principal component as the underlying economic trend that is common to all of the indicator series is an intuitive interpretation that can certainly be challenged. The indicator groups are judgemental, as is the allocation of component series to groups. 


Revisions

The PCEI is subject to revision in subsequent months due to the following reasons (in no particular order):

- Late-coming economic survey data. Sometimes business survey respondents submit data after the close-off date. These data are incorporated in the following month’s edition of the indicator time series. 

- Changes to industry or product classifications. These occur typically every 5-to-10 years and they affect the historical indicator time series data.

- Survey resamplings or redesigns. These occur typically every 5-to-10 years and they affect the historical indicator time series data.

- Recalculation of principal components. This is done every month, when additional indicator series data become available and revised indicator time series data are incorporated for previous months. An alternative, not adopted here, would be to hold the principal component weights fixed for, say, a year.

- Replacement of ARIMA forecasts with actual data. In some cases, when data are not available for the latest month for a particular indicator time series, forecast values are substituted temporarily, calculated with ARIMA models. These forecasts are replaced with actual data the following month, when the data become available. This is done to permit the PCEI to be released in a timely fashion.

- Seasonal adjustment. When one of the indicator time series is seasonally adjusted, its historical values will be revised in subsequent months when the seasonal adjustment is updated.

- Changes to the PCEI definition. From time to time, the list of component time series comprising the PCEI may be changed. This results in a revised PCEI.


The plan is to release updates to the PCEI every month towards the end of the month, incorporating monthly component time series for the period two months back. Thus, for example, the September indicator is released at the end of November. 


Annex - The indicators

The indicators from which the PCEIs are calculated are almost the same for all provinces. Their selection is constrained by what is available on a provincial basis. For example, while total retail sales are available by province, the breakdown by retail sub-industry is not available. The Industry Producer Price Indexes are available nationally, but not by province. The indicators are price deflated and seasonally adjusted where necessary. The allocations to groups are judgemental and many good alternative group assignments or group definitions are also possible. The indicators are as follows:


Production

  • LFS hours worked total and 15 industries
  • United States vehicles entering Canada
  • Electric power generation
  • Wholesale sales
  • Manufacturing sales
  • Exports to United States
  • Production of chicken eggs
  • Milk sold off farms

Labour market

  • LFS unemployment and participation rates
  • LFS total employment
  • SEPH employment total and in 15 industries
  • SEPH Average weekly hours

Investment

  • Housing starts
  • Building permits, residential and non-residential
  • LFS hours worked in construction
  • SEPH employment in construction

Household expenditure and income

  • Average weekly earnings
  • Employment insurance claims received
  • Imports from United States
  • Canadian vehicles returning from United States
  • Relative prices (CPIs relative to all-items CPI) for 8 product classes
  • Restaurant sales
  • Retail sales


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